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The paper Fiber Polytopes by Louis J. Billera and Bernd Sturmfels, published in 1992, presents significant results in polytope theory which open doors to many explorative opportunities. Their results bring together concepts in discrete geometry, combinatorics, algebraic geometry, and theory on polytopal subdivisions. Methods for constructing fiber polytopes provide ways to discover and develop combinatorial structures which contain information about the relationships between known convex polytopes. Fiber polytope theory has also lead to the furthering of our knowledge of triangulations and other types of polytopal subdivisions. This paper offers a self-contained introduction to fiber polytopes and related subjects, while presenting a fascinating and unexpected result by Billera and Sturmfels. The author’s goal is to give undergraduates an accessible and inspiring glimpse of graduate-level geometry.
Withee, Joshua, "Fiber Polytopes" (2015). Honors Theses. 2610.